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T. Gogacz, Y.A. Ibanez Garcia, F. Murlak:
"Finite Query Answering in Expressive Description Logics with Transitive Roles";
in: "Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, Tempe, Arizona, 30 October-2 November 2018.", AAAI Press, 2018, 369 - 378.

We study the problem of finite ontology mediated query an-swering (FOMQA), the variant of OMQA where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We adopt the most typical setting with unions of conjunctive queries and ontologies expressed in description logics (DLs). The study of FOMQA isrelevant in settings that are not finitely controllable. This is the case not only for DLs without the finite model property, but also for those allowing transitive role declarations. When transitive roles are allowed, evaluating queries is challenging: FOMQA is undecidable for SHOIF and only known to be decidable for the Horn fragment of ALCIF. We show decidability of FOMQA for three proper fragments of SOIF: SOI, SOF, and SIF. Our approach is to characterise models relevant for deciding finite query entailment. Relying on a certain regularity of these models, we develop automata-based decision procedures with optimal complexity bounds.

Description Logics; Finite Query answering; Finite Controllability; Automata-based Techniques

https://aaai.org/ocs/index.php/KR/KR18/paper/download/18062/17161